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Numerical Algorithms

Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold

  • 13-09-2024
  • Research
Published in:
Authors
Longfei Wang
Yu Chen
Hongwei Jiao
Yunhai Xiao
Meijia Yang
Published in
Numerical Algorithms | Issue 4/2025

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Abstract

The paper addresses the challenging problem of maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold, a significant area of study in optimization. It introduces the Dinkelbach algorithm to achieve global optimization and presents a specialized linear programming solution for a particular case. The authors also review existing methods, such as semidefinite programming, and compare the computational efficiency of their proposed algorithms with traditional approaches through extensive numerical experiments. The work highlights the practical advantages of the new methods, including reduced computational time and improved scalability.
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previous article Multivariate polynomial interpolation based on Radon projections
next article A posteriori error estimates for the exponential midpoint method for linear and semilinear parabolic equations
Title
Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold
Authors
Longfei Wang
Yu Chen
Hongwei Jiao
Yunhai Xiao
Meijia Yang
Publication date
13-09-2024
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2025
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-024-01939-0
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